2019/12/31 by Masafumi Fukuma, Nobuyuki Matsumoto, Fukuma, Masafumi +3 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Markov Chains and Monte Carlo Methods #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1912.13303
openalex publication_date 2019/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem, where the system is tempered by the antiholomorphic gradient flow to tame both the sign and ergodicity problems simultaneously. In this paper, we implement the hybrid Monte Carlo (HMC) algorithm for transitions on each flowed surface, expecting that this implementation on TLTM will give a useful framework for future computations of large-scale systems including fermions. Although the use of HMC in Lefschetz thimble methods has been proposed so far, our crucial achievement here is that HMC is implemented on TLTM so as to work within the parallel-tempering algorithm in TLTM, especially by developing an algorithm to handle zeros of fermion determinants in the course of the molecular-dynamics process. We confirm that the algorithm works correctly by applying it to the sign problem of the Hubbard model on a small lattice, for which the TLTM is known to work with the Metropolis algorithm. We show that the use of HMC significantly reduces the autocorrelation times with less computational times compared to the Metropolis algorithm.